Large cardinal publications

  • Inner models with large cardinal features usually obtained by forcing
    • A. Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Mathematical Logic, vol. 51, pp. 257-283, 2012. (10.1007/s00153-011-0264-5)  
      Journal Citation arχiv 
      @article {ApterGitmanHamkins2012:InnerModelsWithLargeCardinals,
author = {Apter, Arthur and Gitman, Victoria and Hamkins, Joel David},
affiliation = {Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA},
title = {Inner models with large cardinal features usually obtained by forcing},
journal = {Archive for Mathematical Logic},
publisher = {Springer Berlin / Heidelberg},
issn = {0933-5846},
keyword = {Mathematics and Statistics},
pages = {257--283},
volume = {51},
issue = {3},
url = {http://jdh.hamkins.org/innermodelswithlargecardinals/},
eprint = {1111.0856},
doi = {10.1007/s00153-011-0264-5},
note = {10.1007/s00153-011-0264-5},
year = {2012}
}

  • What is the theory ZFC without power set?
    • V. Gitman, J. D. Hamkins, and T. A. Johnstone, “What is the theory ZFC without Powerset?.” (submitted)  
      Citation arχiv 
      @ARTICLE{GitmanHamkinsJohnstone:WhatIsTheTheoryZFC-Powerset?,
AUTHOR = {Victoria Gitman and Joel David Hamkins and Thomas A. Johnstone},
TITLE = {What is the theory {ZFC} without {Powerset}?},
JOURNAL = {},
YEAR = {},
volume = {},
number = {},
pages = {},
month = {},
note = {submitted},
abstract = {},
keywords = {},
eprint = {1110.2430},
url = {http://arxiv.org/abs/1110.2430},
source = {},
}

  • Generalizations of the Kunen inconsistency
    • J. D. Hamkins, G. Kirmayer, and N. Perlmutter, “Generalizations of the Kunen inconsistency,” to appear in the Annals of Pure and Applied Logic.  
      Citation arχiv 
      @ARTICLE{HamkinsKirmayerPerlmutter:GeneralizationsOfKunenInconsistency,
AUTHOR = {Joel David Hamkins and Greg Kirmayer and Norman Perlmutter},
TITLE = {Generalizations of the {K}unen inconsistency},
JOURNAL = {to appear in the Annals of Pure and Applied Logic},
YEAR = {},
volume = {},
number = {},
pages = {},
month = {},
note = {},
url = {http://arxiv.org/abs/1106.1951},
eprint = {1106.1951},
abstract = {},
keywords = {},
source = {},
}

  • Indestructible strong unfoldability
    • J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame J. Form. Log., vol. 51, iss. 3, pp. 291-321, 2010.  
      Journal MR Citation 
      @ARTICLE{HamkinsJohnstone2010:IndestructibleStrongUnfoldability,
AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
TITLE = {Indestructible strong unfoldability},
JOURNAL = {Notre Dame J. Form. Log.},
FJOURNAL = {Notre Dame Journal of Formal Logic},
VOLUME = {51},
YEAR = {2010},
NUMBER = {3},
PAGES = {291--321},
ISSN = {0029-4527},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2675684 (2011i:03050)},
MRREVIEWER = {Bernhard A. K{\"o}nig},
DOI = {10.1215/00294527-2010-018},
URL = {http://dx.doi.org/10.1215/00294527-2010-018},
file = F
}

  • Tall cardinals
    • J. D. Hamkins, “Tall cardinals,” MLQ Math. Log. Q., vol. 55, iss. 1, pp. 68-86, 2009.  
      Journal MR Citation 
      @ARTICLE{Hamkins2009:TallCardinals,
AUTHOR = {Hamkins, Joel D.},
TITLE = {Tall cardinals},
JOURNAL = {MLQ Math. Log. Q.},
FJOURNAL = {MLQ. Mathematical Logic Quarterly},
VOLUME = {55},
YEAR = {2009},
NUMBER = {1},
PAGES = {68--86},
ISSN = {0942-5616},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {2489293 (2010g:03083)},
MRREVIEWER = {Carlos A. Di Prisco},
DOI = {10.1002/malq.200710084},
URL = {http://dx.doi.org/10.1002/malq.200710084},
file = F
}

  • The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$
    • J. D. Hamkins and T. A. Johnstone, “The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$,” Proc. Amer. Math. Soc., vol. 137, iss. 5, pp. 1823-1833, 2009.  
      Journal MR Citation 
      @ARTICLE{HamkinsJohnstone2009:PFA(aleph_2-preserving),
AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
TITLE = {The proper and semi-proper forcing axioms for forcing notions that preserve {$\aleph_2$} or {$\aleph_3$}},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {137},
YEAR = {2009},
NUMBER = {5},
PAGES = {1823--1833},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2470843 (2009k:03087)},
MRREVIEWER = {John Krueger},
DOI = {10.1090/S0002-9939-08-09727-X},
URL = {http://dx.doi.org/10.1090/S0002-9939-08-09727-X},
file = F
}

  • Large cardinals with few measures
    • A. W. Apter, J. Cummings, and J. D. Hamkins, “Large cardinals with few measures,” Proc. Amer. Math. Soc., vol. 135, iss. 7, pp. 2291-2300, 2007.  
      Journal MR Citation arχiv 
      @ARTICLE{ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures,
AUTHOR = {Apter, Arthur W. and Cummings, James and Hamkins, Joel David},
TITLE = {Large cardinals with few measures},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {135},
YEAR = {2007},
NUMBER = {7},
PAGES = {2291--2300},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {2299507 (2008b:03067)},
MRREVIEWER = {Tetsuya Ishiu},
DOI = {10.1090/S0002-9939-07-08786-2},
URL = {http://dx.doi.org/10.1090/S0002-9939-07-08786-2},
eprint = {math/0603260},
file = F
}

  • Extensions with the approximation and cover properties have no new large cardinals
    • J. D. Hamkins, “Extensions with the approximation and cover properties have no new large cardinals,” Fund. Math., vol. 180, iss. 3, pp. 257-277, 2003.  
      Journal MR Citation arχiv 
      @article{Hamkins2003:ExtensionsWithApproximationAndCoverProperties,
AUTHOR = {Hamkins, Joel David},
TITLE = {Extensions with the approximation and cover properties have no new large cardinals},
JOURNAL = {Fund. Math.},
FJOURNAL = {Fundamenta Mathematicae},
VOLUME = {180},
YEAR = {2003},
NUMBER = {3},
PAGES = {257--277},
ISSN = {0016-2736},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2063629 (2005m:03100)},
DOI = {10.4064/fm180-3-4},
URL = {http://dx.doi.org/10.4064/fm180-3-4},
eprint = {math/0307229},
file = F,
}

  • Exactly controlling the non-supercompact strongly compact cardinals
    • A. W. Apter and J. D. Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” J. Symbolic Logic, vol. 68, iss. 2, pp. 669-688, 2003.  
      MR Citation arχiv 
      @ARTICLE{ApterHamkins2003:ExactlyControlling,
AUTHOR = {Apter, Arthur W. and Hamkins, Joel David},
TITLE = {Exactly controlling the non-supercompact strongly compact cardinals},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {68},
YEAR = {2003},
NUMBER = {2},
PAGES = {669--688},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1976597 (2004b:03075)},
MRREVIEWER = {A. Kanamori},
URL = {http://projecteuclid.org/getRecord?id=euclid.jsl/1052669070},
eprint = {math/0301016},
}

  • A simple maximality principle
    • J. D. Hamkins, “A simple maximality principle,” J. Symbolic Logic, vol. 68, iss. 2, pp. 527-550, 2003.  
      Journal MR Citation arχiv 
      @article{Hamkins2003:MaximalityPrinciple,
AUTHOR = {Hamkins, Joel David},
TITLE = {A simple maximality principle},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {68},
YEAR = {2003},
NUMBER = {2},
PAGES = {527--550},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E40)},
MRNUMBER = {1976589 (2005a:03094)},
MRREVIEWER = {Ralf-Dieter Schindler},
DOI = {10.2178/jsl/1052669062},
URL = {http://projecteuclid.org/getRecord?id=euclid.jsl/1052669062},
month = {June},
eprint = {math/0009240},
}

  • Indestructibility and the level-by-level agreement between strong compactness and supercompactness
    • A. W. Apter and J. D. Hamkins, “Indestructibility and the level-by-level agreement between strong compactness and supercompactness,” J. Symbolic Logic, vol. 67, iss. 2, pp. 820-840, 2002.  
      Journal MR Citation arχiv 
      @ARTICLE{ApterHamkins2002:LevelByLevel,
AUTHOR = {Apter, Arthur W. and Hamkins, Joel David},
TITLE = {Indestructibility and the level-by-level agreement between strong compactness and supercompactness},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {67},
YEAR = {2002},
NUMBER = {2},
PAGES = {820--840},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1905168 (2003e:03095)},
MRREVIEWER = {Carlos A. Di Prisco},
DOI = {10.2178/jsl/1190150111},
URL = {http://dx.doi.org/10.2178/jsl/1190150111},
eprint = {math/0102086},
}

  • Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
    • A. W. Apter and J. D. Hamkins, “Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata,” MLQ Math. Log. Q., vol. 47, iss. 4, pp. 563-571, 2001.  
      Journal MR Citation arχiv 
      @ARTICLE{ApterHamkins2001:IndestructibleWC,
AUTHOR = {Apter, Arthur W. and Hamkins, Joel David},
TITLE = {Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata},
JOURNAL = {MLQ Math. Log. Q.},
FJOURNAL = {MLQ. Mathematical Logic Quarterly},
VOLUME = {47},
YEAR = {2001},
NUMBER = {4},
PAGES = {563--571},
ISSN = {0942-5616},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1865776 (2003h:03078)},
DOI = {10.1002/1521-3870(200111)47:4%3C563::AID-MALQ563%3E3.0.CO;2-%23},
URL = {http://dx.doi.org/10.1002/1521-3870(200111)47:4<563::AID-MALQ563>3.0.CO;2-#},
eprint = {math/9907046}
}

  • The wholeness axioms and $V=\rm HOD$
    • J. D. Hamkins, “The wholeness axioms and $V=\rm HOD$,” Arch. Math. Logic, vol. 40, iss. 1, pp. 1-8, 2001.  
      Journal MR Citation arχiv 
      @article{Hamkins2001:WholenessAxiom,
AUTHOR = {Hamkins, Joel David},
TITLE = {The wholeness axioms and {$V=\rm HOD$}},
JOURNAL = {Arch. Math. Logic},
FJOURNAL = {Archive for Mathematical Logic},
VOLUME = {40},
YEAR = {2001},
NUMBER = {1},
PAGES = {1--8},
ISSN = {0933-5846},
CODEN = {AMLOEH},
MRCLASS = {03E35 (03E65)},
MRNUMBER = {1816602 (2001m:03102)},
MRREVIEWER = {Ralf-Dieter Schindler},
DOI = {10.1007/s001530050169},
URL = {http://dx.doi.org/10.1007/s001530050169},
eprint = {math/9902079}
}

  • The lottery preparation
    • J. D. Hamkins, “The lottery preparation,” Ann. Pure Appl. Logic, vol. 101, iss. 2-3, pp. 103-146, 2000.  
      Journal MR Citation arχiv 
      @article {Hamkins2000:LotteryPreparation,
AUTHOR = {Hamkins, Joel David},
TITLE = {The lottery preparation},
JOURNAL = {Ann. Pure Appl. Logic},
FJOURNAL = {Annals of Pure and Applied Logic},
VOLUME = {101},
YEAR = {2000},
NUMBER = {2-3},
PAGES = {103--146},
ISSN = {0168-0072},
CODEN = {APALD7},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {1736060 (2001i:03108)},
MRREVIEWER = {Klaas Pieter Hart},
DOI = {10.1016/S0168-0072(99)00010-X},
URL = {http://dx.doi.org/10.1016/S0168-0072(99)00010-X},
eprint = {math/9808012}
}

  • Book review of The Higher Infinite, Akihiro Kanamori
    • J. D. Hamkins, “Book review of The Higher Infinite, Akihiro Kanamori,” Studia Logica, vol. 65, iss. 3, pp. 443-446, 2000.  
      Journal Citation 
      @ARTICLE{Hamkins2000:BookReviewKanamori,
AUTHOR = "Joel David Hamkins",
TITLE = "book review of {The Higher Infinite, Akihiro Kanamori}",
JOURNAL = "Studia Logica",
publisher = "Springer Netherlands",
YEAR = "2000",
volume = "65",
number = "3",
pages = "443--446",
month = "",
note = "",
abstract = "",
doi = "10.1023/A:1017327516639",
url = "http://dx.doi.org/10.1023/A:1017327516639",
issn = "0039-3215",
keywords = "",
source = "",
file = F
}

  • Gap forcing: generalizing the Lévy-Solovay theorem
    • J. D. Hamkins, “Gap forcing: generalizing the Lévy-Solovay theorem,” Bull. Symbolic Logic, vol. 5, iss. 2, pp. 264-272, 1999.  
      Journal MR Citation arχiv 
      @article{Hamkins99:GapForcingGen,
AUTHOR = {Hamkins, Joel David},
TITLE = {Gap forcing: generalizing the {L}\'evy-{S}olovay theorem},
JOURNAL = {Bull. Symbolic Logic},
FJOURNAL = {The Bulletin of Symbolic Logic},
VOLUME = {5},
YEAR = {1999},
NUMBER = {2},
PAGES = {264--272},
ISSN = {1079-8986},
MRCLASS = {03E40 (03E55)},
MRNUMBER = {1792281 (2002g:03106)},
MRREVIEWER = {Carlos A. Di Prisco},
DOI = {10.2307/421092},
URL = {http://dx.doi.org/10.2307/421092},
month = {June},
eprint = {math/9901108}
}

  • Universal indestructibility
    • A. W. Apter and J. D. Hamkins, “Universal indestructibility,” Kobe J. Math., vol. 16, iss. 2, pp. 119-130, 1999.  
      MR Citation arχiv 
      @article {ApterHamkins99:UniversalIndestructibility,
AUTHOR = {Apter, Arthur W. and Hamkins, Joel David},
TITLE = {Universal indestructibility},
JOURNAL = {Kobe J. Math.},
FJOURNAL = {Kobe Journal of Mathematics},
VOLUME = {16},
YEAR = {1999},
NUMBER = {2},
PAGES = {119--130},
ISSN = {0289-9051},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {1745027 (2001k:03112)},
MRNUMBER = {1 745 027},
eprint = {math/9808004}
}

  • Superdestructibility: a dual to Laver's indestructibility
    • J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” J. Symbolic Logic, vol. 63, iss. 2, pp. 549-554, 1998. ()  
      Journal MR Citation arχiv 
      @article {HamkinsShelah98:Dual,
AUTHOR = {Hamkins, Joel David and Shelah, Saharon},
TITLE = {Superdestructibility: a dual to {L}aver's indestructibility},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {63},
YEAR = {1998},
NUMBER = {2},
PAGES = {549--554},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {1625927 (99m:03106)},
MRREVIEWER = {Douglas R. Burke},
DOI = {10.2307/2586848},
URL = {http://dx.doi.org/10.2307/2586848},
note = {},
eprint = {math/9612227}
}

  • Small forcing makes any cardinal superdestructible
    • J. D. Hamkins, “Small forcing makes any cardinal superdestructible,” J. Symbolic Logic, vol. 63, iss. 1, pp. 51-58, 1998.  
      Journal MR Citation 
      @article {Hamkins98:SmallForcing,
AUTHOR = {Hamkins, Joel David},
TITLE = {Small forcing makes any cardinal superdestructible},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {63},
YEAR = {1998},
NUMBER = {1},
PAGES = {51--58},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E40 (03E55)},
MRNUMBER = {1607499 (99b:03068)},
MRREVIEWER = {Jakub Jasi{\'n}ski},
DOI = {10.2307/2586586},
URL = {http://dx.doi.org/10.2307/2586586},
}

  • Destruction or preservation as you like it
    • J. D. Hamkins, “Destruction or preservation as you like it,” Ann. Pure Appl. Logic, vol. 91, iss. 2-3, pp. 191-229, 1998.  
      Journal MR Citation 
      @article {Hamkins98:AsYouLikeIt,
AUTHOR = {Hamkins, Joel David},
TITLE = {Destruction or preservation as you like it},
JOURNAL = {Ann. Pure Appl. Logic},
FJOURNAL = {Annals of Pure and Applied Logic},
VOLUME = {91},
YEAR = {1998},
NUMBER = {2-3},
PAGES = {191--229},
ISSN = {0168-0072},
CODEN = {APALD7},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {1604770 (99f:03071)},
MRREVIEWER = {Joan Bagaria},
DOI = {10.1016/S0168-0072(97)00044-4},
URL = {http://dx.doi.org/10.1016/S0168-0072(97)00044-4},
}

  • Canonical seeds and Prikry trees
    • J. D. Hamkins, “Canonical seeds and Prikry trees,” J. Symbolic Logic, vol. 62, iss. 2, pp. 373-396, 1997.  
      Journal MR Citation 
      @article {Hamkins97:Seeds,
AUTHOR = {Hamkins, Joel David},
TITLE = {Canonical seeds and {P}rikry trees},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {62},
YEAR = {1997},
NUMBER = {2},
PAGES = {373--396},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E40 (03E05 03E55)},
MRNUMBER = {1464105 (98i:03070)},
MRREVIEWER = {Douglas R. Burke},
DOI = {10.2307/2275538},
URL = {http://dx.doi.org/10.2307/2275538},
}

  • Fragile measurability
    • J. Hamkins, “Fragile measurability,” J. Symbolic Logic, vol. 59, iss. 1, pp. 262-282, 1994.  
      Journal MR Citation 
      @article {Hamkins94:FragileMeasurability,
AUTHOR = {Hamkins, Joel},
TITLE = {Fragile measurability},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {59},
YEAR = {1994},
NUMBER = {1},
PAGES = {262--282},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1264978 (95c:03129)},
MRREVIEWER = {J. M. Henle},
DOI = {10.2307/2275264},
URL = {http://dx.doi.org/10.2307/2275264},
}

  • Lifting and extending measures; fragile measurability
    • J. D. Hamkins, “Lifting and extending measures; fragile measurability,” PhD Thesis, University of California, Berkeley, Department of Mathematics, 1994.  
      Citation 
      @PHDTHESIS{Hamkins94:Dissertation,
author = {Joel David Hamkins},
title = {Lifting and extending measures; fragile measurability},
institution = {University of California, Berkeley},
year = {1994},
address = {Department of Mathematics},
month = {May},
note = {},
key = {},
crossref = {},
annote = {},
}

  • A class of strong diamond principles
    • J. D. Hamkins, “A class of strong diamond principles,” Preprint, 2002.  
      Citation arχiv 
      @ARTICLE{Hamkins:LaverDiamond,
author = {Joel David Hamkins},
title = {A class of strong diamond principles},
journal = {Preprint},
year = {2002},
eprint = {math/0211419}
}

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